In SIFT a set of keypoints from one image is matched to a set of keypoints in another image by comparing the L2 norm of their residuals [1]}.
Merely using tthe global minimum of the L2 norm produces a lot of false positive matches for the high-dimensional descriptors used in SIFT.
Lowe resorted to matching keypoints only if the ratio of the descriptor distances, \(i.e.\)  square root of the SSR, between the nearest neighbor and second nearest neighbor is lower than \(0.8\) . The threshold of \(0.8\)  is an experimental result after comparing the PDF of correct matches versus the PDF of incorrect matches for different closest to second closest nearest neighbor distances on a database of \(40,000\)  keypoints.
For their object recognition implementation, the threshold eliminated 90% of false matches while discarding less than 5% of the correct matches.
This strategy works well because matches need to have the closest neighbor significantly closer than the closest incorrect match to achieve a reliable matching, hence making the algorithm more robust.
For this reason we decided to also investigate the nearest and second nearest neighbor distances.
